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Which Came First, the Mutation or the Antibiotic?

Understanding Antibiotic Resistance Through Fluctuation Analysis

Suzanne M.  DeschĂȘnes
Department of Biology
Sacred Heart University
Rosemary M. Danaher
Department of Mathematics
Sacred Heart University
Hema Gopalakrishnan
Department of Mathematics
Sacred Heart University


This case study presents the story of Phil, an undergraduate majoring in biology, whose Russian cousin Dimitri has contracted tuberculosis (TB) from inmates at the prison where he works.  Phil learns that his cousin's failure to complete his antibiotic regimen likely contributed to the evolution of antibiotic-resistant TB in his body.  Phil consults with his friend Stacy, and together they try to understand Dimitri's condition by applying what they are learning in their genetics lab experiment about the role of random mutation in bacterial evolution (including the development of antibiotic resistance) through Luria- Delbrück fluctuation analysis. The same analysis includes calculation of the mutation rate, which Phil realizes is sufficient to cause MRSA and other antibiotic-resistant infections. This case study was originally developed for concurrent use in freshman/sophomore-level genetics, elementary statistics, and precalculus. However, it is also very appropriate for courses in introductory biology, evolutionary biology, and biostatistics. The teaching notes discuss various ways to run the case depending on the mathematics and biology background of students.


  • Introduce students to practical real-world examples of mathematical analysis applied to biological processes.
  • Reinforce understanding of mutation frequencies and rates.
  • Increase student awareness of antibiotic resistance in bacterial populations that impact human health.
  • Enable students to distinguish between acquired immunity (i.e., "adaptive mutation") vs random mutation (i.e., evolution by natural selection, driven by random mutation) hypotheses through Luria-Delbrück fluctuation analysis.
  • Provide an introduction to the evolutionary theory that all biology majors will learn in sophomore-level introductory biology courses.
  • Increase student aptitude in data analysis by analyzing the mean, variance, coefficient of variation, mutation frequency and mutation rate.
  • Improve student understanding and appreciation for the exponential and logarithmic functions.
  • Increase student understanding of solving exponential equations using logarithms.


Antibiotic resistance; antibiotic; mutation; mutation rate; Staphylococcus aureus; Staph infection; MRSA; Luria-Delbruck; fluctuation analysis; evolution; Poisson distribution; bacteria

Educational Level

Undergraduate lower division


PDF, Excel

Type Methods

Analysis (Issues), Directed



Subject Headings

Biology (General) Genetics / Heredity Evolutionary Biology Medicine (General) Microbiology Mathematics Statistics

Date Posted


Teaching Notes

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Teaching notes are intended to help teachers select and adopt a case. They typically include a summary of the case, teaching objectives, information about the intended audience, details about how the case may be taught, and a list of references and resources.

Supplemental Materials

Below is the Excel simulation for the Luria-Delbrück fluctuation test used in Part II of the case study.


Answer Key

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